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jfoutz 1016 days ago link
Yeah, that phrase "truly random" in the wikipedia page is misleading. At least they do include in the references a link to Bayer and Diaconis' paper. almost all permuations have never been obtained by a human shuffle. The Bayer Diaconis result implies that for certain types of shuffles the Nike T Shirt For Girls
omaranto 1016 days ago link
codebaobab 1016 days ago linkSort of, depending on what you mean by random. The article seems to imply the uniform distribution on all 52! orders, which 7 shuffles won't get you. For example, you can't reverse a deck with 7 shuffles. There are bets you can put on a deck that's been shuffled 7 times that pay Nike Short Sleeve Dri Fit Shirt
shuffling a deck of cards does not even come close to compl
probability of ending up in U is at least 1 (the total variation distance above)
one, the distance of the shuffled deck to the uniform distribution on all decks tends to zero exponentially fast. So you get a quick change over from "not random at all" to "very random". How many math professors are bona fide magicians?
even if you're preserving blocks of 3, 17! is a big number. it's not 10^44, but still, 10^14 is pretty big.
better than the same bet on a uniformly selected order.
Nice. But of course, shuffling a deck of cards does not even come close to completely randomizing the sequence compared to the previous ordering (especially if you are a crappy shuffler like me). Thus the sequences are correlated, so it's much more complicated to determine how likely it is to get a repeated configuration.
So for Nike Mens Shorts 8 shuffles, we have a probablity of at least 82.4% of landing in U. But for lots of Markov processes, including this Nike Pants Boys
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